Abuse is subjective. If it "feels like abuse" to the receiver, then it's abuse. Third party opinions on the matter are suggestive but not definitive. At any rate, it's manipulative and inconsiderate. That alone is enough to walk, nay run, far far away.
You could send him an e-mail announcing that you're officially broken up and that the matter is not open for discussion. You could refuse to answer any further correspondence. If he refuses to leave you alone, you could get a restraining order.
You could tell him you're planning to get a paternity test for your husband when the baby is born, and that you'll send him a copy either way. Could say that until then, stressing you out is bad for the baby, and that if he actually cares about the baby, he'll leave you alone.
BTW, this stress IS really bad for the baby. There's evidence that shows hormonal conditions in utero affect our long-term development. Babies who are under constant exposure to cortisol (the stress hormone) are more likely to be stressed out as children and adults. So it wouldn't be a bad idea to ask your husband to handle all further contact with him, and for the police to take over where necessary.
Originally Posted by http://www.ohchr.org/en/professionalinterest/pages/crc.aspx
1. The child shall be registered immediately after birth and shall have the right from birth to a name, the right to acquire a nationality and. as far as possible, the right to know and be cared for by his or her parents.
2. States Parties shall ensure the implementation of these rights in accordance with their national law and their obligations under the relevant international instruments in this field, in particular where the child would otherwise be stateless.
Nadya's correct that in some jurisdictions, the husband of the mother is the legal father of the child. This does not violate the UN Convention on the Rights of the Child, because in these jurisdictions, that man is the "parent." If it were otherwise, anonymous sperm donation and closed adoptions would be outlawed.
So, OP, it might be worth the legwork to find out if you're in one of these jurisdictions. If so, you can cut all ties and tell him to go fuck his paternity test.